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Consider the production function Q = 48L2 – 2L3 with associated MPL = 96L6L2 . At...

Consider the production function Q = 48L2 – 2L3 with associated MPL = 96L6L2 . At what value of L

a. is average product at its maximum?

b. is marginal product at its maximum?

c. is total product at its maximum?

d. do diminishing marginal returns set in?

e. What is the value of Q when it is as its maximum?

f. What is the value of Q when diminishing marginal returns set in?

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Answer #1

Consider the production function Q = 48L^2 – 2L^3 with associated MPL = 96L - 6L^2 .

At what value of L

a. is average product at its maximum?

Average product = Q/L = 48L - 2L^2

Maximize AP to give

48 - 4L = 0

L* = 48/4 = 12 units.

b. is marginal product at its maximum?

Set the derivative of MP = 0

96 -12L = 0

L = 96/12 = 8 units

c. is total product at its maximum?

Total product is maximum when MP is 0

96L - 6L^2 = 0

16 - L = 0

Which gives L = 16.

d. do diminishing marginal returns set in?

After L = 8 because teh marginal product starts falling.

e. What is the value of Q when it is as its maximum?

Q =  48*(16^2) – 2*(16^3)

= 4096

f. What is the value of Q when diminishing marginal returns set in?

Q =   48*(8^2) – 2*(8^3)

= 2048

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